 reserve i,j,n,k,l for Nat;
 reserve T,S,X,Y,Z for Subset of MC-wff;
 reserve p,q,r,t,F,H,G for Element of MC-wff;
 reserve s,U,V for MC-formula;
reserve f,g for FinSequence of [:MC-wff,Proof_Step_Kinds_IPC:];

theorem :: Modus Ponens for valid_IPC
  p is valid_IPC & p => q is valid_IPC implies q is valid_IPC
proof
A1: IPC-Taut is IPC_theory;
  assume p is valid_IPC & p => q is valid_IPC;
  then p in IPC-Taut & p => q in IPC-Taut;
  hence thesis by A1;
end;
